Conjugacies between ergodic transformations and their inverses
Goodson, Geoffrey
Colloquium Mathematicae, Tome 84/85 (2000), p. 185-193 / Harvested from The Polish Digital Mathematics Library
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We study certain symmetries that arise when automorphisms S and T defined on a Lebesgue probability space (X, ℱ, μ) satisfy the equation ST=T-1S. In an earlier paper [6] it was shown that this puts certain constraints on the spectrum of T. Here we show that it also forces constraints on the spectrum of S2. In particular, S2 has to have a multiplicity function which only takes even values on the orthogonal complement of the subspace f∈L2(X,ℱ,μ):f(T2x)=f(x). For S and T ergodic satisfying this equation further constraints arise, which we illustrate with examples. As an application of these results we give a general method for constructing weakly mixing rank one maps T for which T2 has non-simple spectrum.

Publié le : 2000-01-01
EUDML-ID : urn:eudml:doc:210796 
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Goodson, Geoffrey. Conjugacies between ergodic transformations and their inverses. Colloquium Mathematicae, Tome 84/85 (2000) pp. 185-193. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv84i1p185bwm/

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